Graphing Linear Inequalities in Two Variables MATH 018 Combined Algebra S. Rook

2 Overview Section 3.6 in the textbook –Determining whether a Point Satisfies an Inequality –Graphing Linear Inequalities Including finding test points and shading

Determining whether a Point Satisfies an Inequality

4 Linear Inequality: an INEQUALITY in which ALL variables are raised to the first power –e.g. 2x – y ≥ 3 Given a linear inequality and a point (x, y), how would we determine whether the point satisfied the inequality? –e.g. Does (3, 3) satisfy 2x – y ≥ 3?

Determining whether a Point Satisfies an Inequality (Example) Ex 1: Determine whether each point satisfies 3x + 5y < -3 a) (-1, 0) b) (-5, -2) 5

Graphing Linear Inequalities

7 We know 3 ways to graph: –Table of Values –Intercepts –By slope and y-intercept No different when graphing linear inequalities EXCEPT for: –Whether the line is solid (≤, ≥) or broken ( ) –Shading one side of the line to indicate the solution set

8 Test Points and Shading After constructing the line, pick a test point that does NOT lie on the line Any point will do, but (0, 0) is often a good choice EXCEPT when it lies on the line Determine whether the test point makes the inequality true: –If the inequality is true, shade the side of the line WITH the test point –If the inequality is false, shade the side of the line WITHOUT the test point

Graphing Linear Inequalities (Example) Ex 2: Graph the linear inequality: a)x – 4y > 8 b)y ≥ 2x c)4x + 6y < -10 d)-5x – 3y ≤ 15 9

10 Summary After studying these slides, you should know how to do the following: –Determine whether a point satisfies a linear inequality –Graph a linear inequality on a coordinate grid and correctly shade one side of the line based on a test point Additional Practice –See the list of suggested problems for 3.6 Next lesson –Solving Systems of Equations by Graphing (Section 4.1)